A306026 Antidiagonal sums of A306024.

1, 1, 2, 5, 16, 66, 343, 2180, 16505, 145773, 1477880, 16986349, 219158316, 3147962668, 49982588535, 871766923048, 16609804758449, 344016348602845, 7711752589539436, 186379711851775401, 4839449174872615116, 134575228738532130948, 3996183953610068510929

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..200

Formula

a(n) = Sum_{j=0..n} j! * [x^j] exp(Sum_{i=1..n-j} (exp(i*x)-1)/i).

a(n) = Sum_{j=0..n} A306024(j,n-j).

Maple

b:= proc(n, k, m) option remember; `if`(n=0, 1,
      add(b(n-1, k, max(m, j)), j=1..m+k))
    end:
a:= n-> add(b(j, n-j, 0), j=0..n):
seq(a(n), n=0..25);
# second Maple program:
b:= (n, k)-> n!*coeff(series(exp(add((exp(j*x)-1)/j, j=1..k)), x, n+1), x, n):
a:= n-> add(b(j, n-j), j=0..n):
seq(a(n), n=0..25);

Crossrefs

Cf. A306024, A305971.

Sequence in context: A000522 A182290 A007469 * A091139 A084785 A124551

Adjacent sequences: A306023 A306024 A306025 * A306027 A306028 A306029

Keyword

nonn

Author

Alois P. Heinz, Jun 17 2018

Status

approved